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D. Fields

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  1. D.1 Gravitational fields

    1. D.1.1—Kepler’s three laws of orbital motion

      • Kepler’s three laws of orbital motion.

    2. D.1.2—Universal gravitation

      • Universal gravitation: F=Gm1m2/r^2 for point masses.

    3. D.1.3—Point-mass approximation

      • Extended bodies can be treated as point masses only under suitable conditions.

    4. D.1.4—Gravitational field strength

      • Gravitational field strength: g=F/m=GM/r^2.

    5. D.1.5—Gravitational field lines

      • Gravitational field lines.

    6. D.1.6 (HL)—Gravitational potential energy

      • Gravitational potential energy is work to assemble masses from infinite separation.

    7. D.1.7 (HL)—Two-body potential energy

      • Two-body gravitational potential energy: Ep=-Gm1m2/r.

    8. D.1.8 (HL)—Gravitational potential

      • Gravitational potential: Vg=-GM/r, zero at infinity.

    9. D.1.9 (HL)—Potential gradient

      • Field strength is potential gradient: g=-ΔVg/Δr.

    10. D.1.10 (HL)—Work in gravitational fields

      • Work in gravitational field: W=mΔVg.

    11. D.1.11 (HL)—Gravitational equipotentials

      • Equipotential surfaces for gravitational fields.

    12. D.1.12 (HL)—Equipotentials and field lines

      • Relationship between equipotential surfaces and gravitational field lines. • Equipotential surfaces are perpendicular to field lines.

    13. D.1.13 (HL)—Escape speed

      • Escape speed: vesc=sqrt(2GM/r).

    14. D.1.14 (HL)—Orbital speed

      • Circular orbital speed: vorbital=sqrt(GM/r).

    15. D.1.15 (HL)—Atmospheric drag on orbits

      • Small atmospheric drag changes both height and speed of an orbiting body.

  2. D.2 Electric and magnetic fields

    1. D.2.1—Electric charge forces

      • Direction of forces between the two types of electric charge.

    2. D.2.2—Coulomb’s law

      • Coulomb’s law: F=kq1q2/r^2 for point charges; k=1/(4πε0).

    3. D.2.3—Charge conservation

      • Conservation of electric charge.

    4. D.2.4—Millikan experiment

      • Millikan’s experiment as evidence for quantization of electric charge.

    5. D.2.5—Charge transfer

      • Charge transfers by friction, electrostatic induction or contact. • Grounding can remove or add charge.

    6. D.2.6—Electric field strength

      • Electric field strength: E=F/q.

    7. D.2.7—Electric field lines

      • Electric field lines.

    8. D.2.8—Field-line density

      • Relationship between field line density and field strength. • Greater field-line density indicates stronger field.

    9. D.2.9—Parallel-plate field

      • Uniform field between plates: E=V/d.

    10. D.2.10—Magnetic field lines

      • Magnetic field lines.

    11. D.2.11 (HL)—Electric potential energy

      • Electric potential energy is work to assemble charges from infinite separation.

    12. D.2.12 (HL)—Two-charge potential energy

      • Two-charge electric potential energy: Ep=kq1q2/r.

    13. D.2.13 (HL)—Electric potential as scalar

      • The electric potential is a scalar quantity with zero defined at infinity.

    14. D.2.14 (HL)—Electric potential

      • Electric potential: Ve=kQ/r, zero at infinity.

    15. D.2.15 (HL)—Electric potential gradient

      • Electric field strength is potential gradient: E=-ΔVe/Δr.

    16. D.2.16 (HL)—Work in electric fields

      • Work moving charge in electric field: W=qΔVe.

    17. D.2.17 (HL)—Electric equipotentials

      • Equipotential surfaces for electric fields. • No work is done moving along an equipotential surface.

    18. D.2.18 (HL)—Equipotentials and electric fields

      • Relationship between equipotential surfaces and electric field lines. • Equipotential surfaces are perpendicular to electric field lines.

  3. D.3 Motion in electromagnetic fields

    1. D.3.1—Charge in electric fields

      • Motion of a charged particle in a uniform electric field.

    2. D.3.2—Charge in magnetic fields

      • Motion of a charged particle in a uniform magnetic field.

    3. D.3.3—Crossed electric and magnetic fields

      • Charged particles can move in perpendicular uniform electric and magnetic fields.

    4. D.3.4—Magnetic force on charge

      • Magnetic force on moving charge: F=qvB sinθ.

    5. D.3.5—Force on current conductor

      • Force on current-carrying conductor: F=BIL sinθ.

    6. D.3.6—Force between parallel wires

      • Force per unit length between parallel wires: F/L=μ0I1I2/(2πr). • Parallel currents attract when currents flow in the same direction.

  4. D.4 Induction

    1. D.4.1 (HL)—Magnetic flux

      • Magnetic flux: Φ=BA cosθ.

    2. D.4.2 (HL)—Faraday’s law

      • Faraday’s law: changing magnetic flux induces emf ε=-NΔΦ/Δt.

    3. D.4.3 (HL)—Motional emf

      • Motional emf in a straight conductor: ε=BvL.

    4. D.4.4 (HL)—Lenz’s law

      • Lenz’s law gives induced emf direction and reflects energy conservation. • Direction of induced emf opposes the change that produces it.

    5. D.4.5 (HL)—Rotating-coil emf

      • Rotating coil in uniform magnetic field produces sinusoidal emf.

    6. D.4.6 (HL)—Rotation frequency and emf

      • Increasing rotation frequency increases induced emf characteristics.